The

# Hot Hand Fallacy

, explained.
Bias

## What is the Hot Hand Fallacy?

The hot hand fallacy is the tendency to believe that someone who has been successful in a task or activity is more likely to be successful again in further attempts. The hot hand fallacy derives from the saying that athletes have “hot hands” when they repeatedly score, causing people to believe that they are on a streak and will continue to have successful outcomes.

## Where this bias occurs

Imagine you are watching a hockey game, and a goalie makes five saves in the opening few minutes. We predict that the goalie will continue making saves because they are on a “hot streak.”

We base our prediction on a small run of random events without considering that the goalie’s first five saves could have been chance. We assume they are on a streak because we mistakenly believe that a short pattern is representative of a larger sample. The hot hand fallacy leads us to take a small pool of data—the opening minutes of one game—as a better indicator of future performance than an average save percentage calculated from seasons’ worth of data.

## Individual effects

The hot hand fallacy is most commonly discussed within the context of sports or gambling. While making incorrect predictions may not have negative consequences alone, people often place bets on these outcomes. And once money becomes involved, these incorrect predictions can begin to have more serious consequences.

If we make a bet on a sports game based on a successful run in the first ten minutes, we are putting money down without considering all of the data. Just because a team or player is performing unusually well for a short period does not counter their average statistics—but the hot hand fallacy makes us believe it does. We are likely to lose bets when basing them on illogical fallacies.

Fans are not the only people susceptible to the hot hand fallacy. Managers and coaches often make decisions based on a small sample of observations, such as which players should be part of the starting line-up. Even players choose which teammates to pass to with only recent plays in mind. In this way, the hot hand fallacy determines not only the bets placed on a game, but the outcome of the game itself.

Similarly, when we have a winning streak in gambling, we assume that our success will continue. In reality, most gambling games involve chance, and subsequent performance is completely independent of previous performance. We might get careless with our bets when we trust our good luck will continue, losing all of our stakes in the process.

## Systemic effects

The problem with the hot hand fallacy is that our fallacious reasoning affects others.We often behave according to other people’s predictions, such as deciding what to wear based on the weatherman’s forecast, or investing in stocks based on economists’ anticipated trends. This means that if these public predictions are based on incorrect reasoning, their negative consequences will spread like wildfire.

But these widespread impacts do not end at an individual level. The hot hand fallacy even dictates how we shape our systems.

Consider how politicians become delegates: by winning primaries. Suppose your favorite politician comes on top several primaries in a row. We may conclude they will win the general election, even if this sample does not represent the overall percentage of primaries they are likely to win. Our false assumption may cause us to change our vote, assuming the politician no longer needs our support. Other candidates may even drop out of the race, believing they don’t stand a chance. In this case, our miscalculations decide who will run our government for the foreseeable future.

## How it affects product

We love using apps to track our progress, whether that be counting our steps or measuring how many words we’ve learned in a new language. With our habits meticulously monitored and statics automatically charted, you would think that we would be better than ever at gauging our future success.

However, habit tracker apps may make us even more likely to fall victim to the hot hand fallacy. For instance, if you notice that you’ve taken over 20,000 steps for the last three days, you may assume your fitness streak will sustain—even if your usual daily average is half that amount. Or you might predict you will master German in the next year, since you’ve learned 25 new words a day for the past week (despite this being a new personal record). In both scenarios, our heightened awareness of consecutive successes may make us confident that more is to come, which unfortunately is never guaranteed.

That is not to say that humans cannot pick up new habits. As we put in more effort, it makes sense that our daily average of steps taken or words learned would grow over time. However, learning skills are never linear. There will always be ups and downs in our curve towards success. But the hot hand fallacy may cause us to only anticipate the upward trends when using these apps, rather than preparing us for the dips yet to come.

## Hot hand fallacy and AI

Machine learning is prone to error, just like its human creators. However, when algorithms chug out numerous high-quality outputs in a row, we may expect the same level of quality for all future outputs. Statistically speaking, perfection is impossible: the technology is too recent, and the datasets it draws from are full of flaws. But thanks to the hot hand fallacy, we may refrain from fact-checking and accept miscalculations as a continuing hot streak.

Let’s look at an example: hiring in the workforce. Most companies rely on machine learning to conduct the initial review of candidates, such as scanning their resumes for desirable skills. If an AI hiring tool selects numerous good candidates in a row, hiring managers may expect the same future success rate when choosing contenders to move onto the interview process.

However, hiring managers may be disappointed when the algorithm eventually fails by choosing some not-so-impressive candidates. Or, even worse, hiring managers may be missing out on potentially even better candidates with resumes too sophisticated for the AI hiring tool to identify. Nevertheless, over-relying on machine learning due to the hot hand fallacy might make us neglect the human touch many processes still require.

## Why it happens

As humans, we tend to try and identify trends to make sense of the world. However, this tendency makes it difficult for us to understand chance because we combine data into patterns that don’t exist. By ignoring probability, we deduce that independent events are dependent on one another.1

We can further explain the hot hand fallacy using the law of small numbers.2 We often believe that small samples represent the larger samples they are drawn from. After all, this is why behavioral science relies on random sampling, since it is too difficult to study the entire relevant population. However, these samples often show patterns that don’t exist in greater sequences.

Surprisingly, small numbers often don’t behave the way that large numbers behave. For example, it isn’t that unlikely that we would get five heads in a row in a coin toss when we only toss it five times. Yet we think this is a hot streak, since there is a 50/50 chance of getting heads or tails—but we only got heads. However, if we continued to toss the coin 100 times, we are likely to have an overall number of heads closer to 50%, even if each smaller portion of the larger sequence does not necessarily reflect this.2

## Why it is important

The hot hand fallacy leads us towards suboptimal decisions based on faulty reasoning instead of logic and rationality. We misidentify patterns and base subsequent choices on these made-up trends.

Although the hot hand fallacy is most commonly researched in sports and gambling contexts, it can also impact day-to-day behavior. If we feel as though we have been lucky recently, we may spontaneously make decisions based on that feeling. We may buy a lottery ticket and pick numbers based on last week’s winning ticket, even though neither our past luck nor the past winning numbers actually determine our likelihood of winning today’s draw.

The hot hand fallacy is also dangerous because it impacts consumer behavior. One study conducted by Joseph Johnson found that consumers are more likely to buy into a stock when it has been experiencing a positive earning trend.3 However, a previous trend is only based on a three-to-seven-day period and does not reflect the overall up and down pattern. This means a stock could crash right after you invest in it, no matter how well it was doing before.

## How to avoid it

Being aware of the hot hand fallacy can help us think twice before basing our decisions on a small amount of data like a winning streak.

Overcoming cognitive heuristics is difficult because we have to look somewhere for rationale when making decisions. To ensure that the hot hand fallacy does not override logical reasoning, we turn to larger sets of data when making predictions about future performance.

For example, we might be tempted to place a bet on a basketball game based on our favorite player’s three successful baskets in the first ten minutes of the game. However, we can remind ourselves to look at statistics representing a much larger data set like his season average. This way, we can make more intelligent predictions.

## How it all started

The hot hand fallacy was first described in 1985 by behavioral scientists Amos Tversky, Thomas Gilovich, and Robert Vallone.1 The group described the mistakes that we often make believing that we can make predictions about future outcomes based on a small sample of previously successful outcomes. They examined this heuristic regarding the term “hot hands” in basketball, where we believe a player making baskets will continue to do so.

As the researchers described, fans, coaches, and even players seem to believe that a player’s performance at the beginning is a predictor of their performance in the rest of the game, overshadowing their statistics. Let’s say, for example, a player makes their first three shots in a basketball game, but their average success rate is 75%. Instead of realizing that the first three baskets were random successes, we are likely to think that the player has “hot hands” and his success will continue in subsequent shots.

## Hot hand fallacy controversies

There is no debate on whether the hot hand fallacy exists. All the evidence supports that we tend to overestimate future successes after a winning streak. What is contested is the hot hand effect—that is, whether sometimes we actually do have more successes after a winning streak.

The original research by Tversky, Gilovich, and Vallone in 1985 proposed that having hot hands in basketball was merely a cognitive fallacy. Players weren’t actually riding the high of their success, the fans just perceived they were. The odds were still statistically the same.

However, a 2018 paper by Joshua Miller and Adam Sanjurjo suggested this might not be true. Ironically, they identified a bias in the original 1985 study’s methodology, which made real winning streaks seem like a random sequence of hits and misses. This finding sparked lots of debate amongst behavioral scientists, forcing them to reconsider what they once considered a given. Maybe the hot hand effect was a thing, after all.

Since then, further statistical research spanning the past decade answers: it just might be. These studies examined winning streaks across a variety of professional sports, ranging from the classic basketball example to other examples like baseball. When researchers controlled for the hot hand fallacy, they still were able to identify the hot hand effect.7,8 In other words, players with winning streaks truly did have an increased chance of making the next play. So maybe sports fans weren’t crazy for cheering on their favorite players after all!

It is worth noting two things about this research. First, this research is brand new and results from various statistical methodologies and interpretations. This means it may be a while until we know for sure whether the hot hand effect actually exists or not. Second, this research only focuses on human performances in sports. This means that the hot hand effect may not exist in other contexts depending more on probability, such as when flipping a coin or rolling a dice.

## Example 1 – The hot hand fallacy increases as we age

To try and understand what causes the hot hand fallacy, Dr. Alan Castel, a Professor of Psychology at UCLA, examined whether age is a moderator.4

There is a common belief in behavioral science that the older we get, the more we rely on heuristics for making decisions. With this in mind, Castel hypothesized older adults would be more likely to predict that a player will make a third successful shot after they had made two successful shots.

The study began by telling participants ranging from 22-90 years old that NBA players make around 50% of their shots. Next, they were asked the following two questions:

1. Does a basketball player have a better chance of making a shot after having just made the last two shots than after having missed the last two shots?
2. Is it important to pass the ball to someone who has just made a few shots in a row?

Castel found that older participants were more likely to answer yes to both questions, suggesting they were influenced more by the hot hand fallacy than younger participants.4

The study provides evidence that older people are more likely to rely on heuristic-based processing, even though they likely have more experience with random sequence events. These results warn that awareness of the hot hand fallacy might not be enough to counter it as with age, and more drastic measures might be necessary to avoid faulty predictions.

## Example 2 – The hot hand fallacy and human agency

The hot hand fallacy seems to be the opposite of the gambler's fallacy, which suggests future outcomes will be different than previous outcomes. To better understand this discrepancy, Peter Ayton and Ilan Fischer tried to determine in which situations each fallacy is more likely to occur.5

The researchers showed participants a computer generated roulette wheel that they spun after betting which color the spinner would land on. When making their predictions, participants also had to rate their confidence levels as either “no confidence” or “strong confidence.”

The researchers found that when a certain color had a streak, participants were likely to be influenced by the gambler’s fallacy and believe the next spin would result in the opposite color. However, the confidence level reports suggested that a past run of successful predictions led to increased confidence levels in future predictions.5

From these results, Ayton and Fischer concluded that the hot hand fallacy is more likely to influence decision-making when people are considering human performance. Meanwhile, the gambler’s fallacy is more likely to impact gambling decisions based on inanimate mechanisms like the roulette wheel.

However, the experiment does not explain why we experience the hot hand fallacy in situations that involve inanimate mechanisms we are not betting on. Participants in gambling situations may behave differently than people who are just trying to guess heads or tails in a coin toss.

## Summary

##### What it is

The hot hand fallacy describes our tendency to believe that a successful streak is likely to lead to further success. For example, if a basketball player has made three consecutive shots, we may believe he has a greater chance of making the fourth than he actually does.

##### Why it happens

The hot hand fallacy occurs because we believe that small samples of data are representative of larger samples of data, when this really is not the case. We often look for patterns in sequences and find it hard to understand chance, causing us to make illogical predictions.

##### Example 1 - The hot hand fallacy increases with age

Many psychologists believe that the older we get, the more we rely on heuristics in our decision-making processes. Evidence supporting this theory indicates older people are more likely to be misled by the hot hand fallacy when it comes to predicting the future performance of basketball players when they’ve had a successful streak.

##### Example 2 - The hot hand fallacy influences predictions based on human skill

The hot hand fallacy seems to contradict the gambler’s fallacy, which suggests future outcomes will be different than previous outcomes. The hot hand fallacy may be caused by increased confidence in our ability to predict what will happen when we have made a run of successful predictions. Alternatively, the gambler’s fallacy may be more likely to occur when we believe outcomes are only influenced by inanimate mechanisms, not human skill.

##### How to avoid it

As the hot hand fallacy is based on the law of small numbers, we can try and make predictions based on larger data pools. Considering more statistics makes us less likely to identify patterns that don’t actually exist, allowing us to anticipate outcomes more accurately.

## Related TDL articles

##### Why We See Gambles as Certainties

In this article, Stefan Kelly explores the different biases that cause people to believe they can be confident in their gambling. He suggests people often mistake themselves as skilled gamblers, sometimes caused by the hot hand fallacy. Kelly points out that awareness of gambling biases does little to deter gamblers or their habits, demonstrating that heuristics often overpower rationality.

##### Why do we think a random event is more or less likely to occur if it happened several times in the past?

This article breaks down the gambler’s fallacy, which is when we mistakenly believe that future outcomes will differ from a series of previous outcomes. Many consider this bias to be the “antonym” of the hot hand fallacy. Read on to learn about the kind of situations where we will likely fall for the gambler’s fallacy instead.

## Sources

1. Tversky, A, Gilovich, T. & Vallone, R. (1985). The hot hand in basketball: On the misperception of random sequences. Cognitive Psychology, 17(3), 295-314. https://doi.org/10.1016/0010-0285(85)90010-6
2. IResearchNet.com. (2016, January 21). Law of small numbers. Psychology. Retrieved August 12, 2020, from https://psychology.iresearchnet.com/social-psychology/decision-making/law-of-small-numbers
3. Johnson, J., Tellis, G. J., & Macinnis, D. J. (2005). Losers, winners, and biased trades. Journal of Consumer Research, 32(2), 324-329. https://doi.org/10.1086/432241
4. Castel, A. D., Rossi, A. D., & McGillivray, S. (2012). Beliefs about the “hot hand” in basketball across the adult life span. Psychology and Aging, 27(3), 601-605. https://doi.org/10.1037/a0026991
5. Ayton, P., & Fischer, I. (2004). The hot hand fallacy and the gambler’s fallacy: Two faces of subjective randomness? Memory & Cognition, 32(8), 1369-1378. https://doi.org/10.3758/bf03206327
6. Miller, J. B., & Sanjurjo, A. (n.d.). Surprised by the Hot Hand Fallacy? A Truth in the Law of Small Numbers.
7. Bocskocsky, A., Ezekowitz, J., & Stein, C. (2014). Heat Check: New Evidence on the Hot Hand in Basketball (SSRN Scholarly Paper No. 2481494). https://doi.org/10.2139/ssrn.2481494
8. Glazer, A., & Goldberg, L. R. (2020). Hot or Not? A Nonparametric Formulation of the Hot Hand in Baseball (SSRN Scholarly Paper No. 3562754). https://doi.org/10.2139/ssrn.3562754

### Dan Pilat

Dan is a Co-Founder and Managing Director at The Decision Lab. He is a bestselling author of Intention - a book he wrote with Wiley on the mindful application of behavioral science in organizations. Dan has a background in organizational decision making, with a BComm in Decision & Information Systems from McGill University. He has worked on enterprise-level behavioral architecture at TD Securities and BMO Capital Markets, where he advised management on the implementation of systems processing billions of dollars per week. Driven by an appetite for the latest in technology, Dan created a course on business intelligence and lectured at McGill University, and has applied behavioral science to topics such as augmented and virtual reality.

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Sekoul is a Co-Founder and Managing Director at The Decision Lab. He is a bestselling author of Intention - a book he wrote with Wiley on the mindful application of behavioral science in organizations. A decision scientist with a PhD in Decision Neuroscience from McGill University, Sekoul's work has been featured in peer-reviewed journals and has been presented at conferences around the world. Sekoul previously advised management on innovation and engagement strategy at The Boston Consulting Group as well as on online media strategy at Google. He has a deep interest in the applications of behavioral science to new technology and has published on these topics in places such as the Huffington Post and Strategy & Business.

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